On Finite Delay-Moment Conditions in Queues

We review the Kiefer–Wolfowitz conditions for finite delay moments at a GI/G/s queue, which are independent of moment conditions on the arrival process. Through examples, we show that for nonrenewal arrivals, some additional conditions on the arrival process are necessary. We discuss the question of whether some known sufficient conditions for finite delay moments at “downstream” stations in a tandem queue are really necessary. We then show how to decouple conditions on the arrival process from conditions on service times. Finally, we obtain sufficient conditions for queues with regenerative arrivals.